Transformation groups of certain flat affine manifolds

Abstract

In this paper we characterize the group of affine transformations of a flat affine simply connected manifold whose developing map is a diffeomorphism. This is proved by making use of some simple facts about homeomorphisms of ${\mathbb{R}}^n$ preserving open connected sets. We show some examples where the characterization is useful.

This is a preprint of an article published in Sao Paulo Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s40863-021-00223-6